# Math (MATH)

**MATH 502**

**Math for Our World**

**(4 Credits)**

This course takes an integrated approach to the study of mathematics, combining mathematical concepts with applications in the real world. It addresses topics in mathematics necessary in a college education, providing the reasoning strategies needed for mathematical problem solving in the workplace, the media, and everyday life. The course serves as the foundation for higher-level math courses and provides the quantitative skills necessary to be adequately prepared for coursework in other academic areas. The overarching goal is to learn to interpret quantitative and statistical information that we encounter daily. Students will understand how real-world problems can be analyzed using the power and rigor of mathematical and statistical models. Topics include: problem solving, math of finance, geometry, basic probability, and beginning statistical concepts with an emphasis on real world applications and interpreting information. The use of Excel will be incorporated into the topics of this course.

**Prerequisite(s):**Acceptable scores on Accuplacer Arithmetic and Elementary Algebra Accuplacer Classic or Next Generation Accuplacer assessments; or approved exemption based on previous high school transcripts: a grade of C or better in both Algebra and Geometry taken within the last five years; or SAT Math score of 500+ or ACT Math score of 18+ taken within five years of registration; or successful completion of the ALEKS Program Math Tutorial as determined by Granite State College Math faculty. Accuplacer or ALEKS assessments should be completed within five years of registering for course.

**MATH 504**

**Statistics**

**(4 Credits)**

This course addresses introductory statistical concepts, methods, and procedures important for making well informed decisions in real world settings. It provides students with both theoretical principles and practical skills in statistics. Topics include an overview of descriptive and inferential statistics, specifically sampling, measurements of central tendency and dispersion, frequency distributions, graphing techniques, probability theory, hypothesis testing, normal distribution, regression and correlation, t-tests, and analysis of variance.

**Prerequisite(s):**MATH 502 Math for Our World or an acceptable score on the Classic or Next Generation Accuplacer arithmetic and elementary algebra assessment. Accuplacer assessments should be completed within five years of registering for course. NOTE: Excel proficiency is expected prior to enrollment in this course.

### View Course Outcomes:

- Recognize and demonstrate the use of best practices in design of experiments including sampling procedures and data collection methods.
- Construct and interpret basic data visualization techniques, such as frequency distributions, bar charts, histograms, boxplots, scatterplots, and time series.
- Compute and evaluate measures of central tendency and dispersion including means, medians and modes; and variance, standard deviations, z-scores, and percentiles.
- Perform and interpret a correlation and a linear regression analysis.
- Identify and apply basic probability rules and characteristics of discrete and continuous probability distributions to solve and interpret real-world problems.
- Explain the concepts of confidence interval and statistical significance based on comprehension of the underlying principles of probability theory.
- Explain how sample statistics and sampling distributions are used to estimate population parameters and draw inferences.
- Construct and interpret confidence intervals.
- Formulate and perform hypothesis testing in real-world situations. 1
- Using real-world data, perform and interpret tests such as t-tests and one-way analysis of variance. 1
- Analyze and demonstrate an understanding of current ethical standards that pertain to the use of statistical methods, data, and research results.

**MATH 510**

**Pre-Calculus**

**(4 Credits)**

This course is intended as a bridge course between algebra and calculus. The course focuses on strengthening the student's mathematical problem solving skills and developing a firm understanding of functions, their graphical representation, their behavior, and their use to model real-life situations. Various classes of functions will be highlighted: polynomials, rational, exponential, logarithmic, and trigonometric. Topics may also include: algebraic concepts, real number system, systems of equations and inequalities, complex numbers, and polar coordinates.

**Prerequisite(s):**MATH 502 Math for Our World or an acceptable score on the Classic or Next Generation Accuplacer assessment(s). Accuplacer assessments should be completed within five years of registering for course. A graphing calculator is required.

### View Course Outcomes:

- Define a function verbally, numerically, visually, and algebraically as well as define and find its domain and range.
- Perform operations on functions such as: addition, multiplication, division, composition,and finding inverse functions.
- Graph and specify the algebraic characteristics of polynomial, rational, radical, exponential, logarithmic, and trigonometric functions, both by hand and by graphing calculators.
- Identify the characteristics of the conic sections, both graphically and algebraically.
- Manipulate and evaluate algebraic, exponential, logarithmic and trigonometric functions.
- Employ mathematical modeling techniques to solve problems using polynomial, rational, radical, exponential, logarithmic, and trigonometric functions.
- Solve problems involving the intermediate value theorem, the division algorithm of polynomials, the remainder theorem, the factor theorem, and zeros of a polynomial.
- Solve problems involving systems of equations and inequalities in two unknowns.
- Interpret and define the six trigonometric functions, in terms of both right triangles and the unit circle. 1
- Graph trigonometric and inverse trigonometric functions, with and without the aid of a graphing calculator. 1
- Verify and apply trigonometric identities and formulas and apply them to solve trigonometric equations and word problems. 1
- Gain skill in the use of polar coordinates, specifically perform conversions between polar and Cartesian coordinates and sketch graphs of polar curves in both Cartesian and polar coordinates both by hand and using technology.

**MATH 600**

**Mathematical Proof**

**(4 Credits)**

This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Methods of problem solving will be based on Polya’s four steps for problem solving. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics chosen from the following areas: functions and relations, set theory, number theory, and logic, Euclidian and non-Euclidian geometry, algebra, mathematical reasoning, proof, and problem solving. Connections to middle and secondary school mathematics.

**Prerequisite(s):**MATH 510 Pre-Calculus.

### View Course Outcomes:

- Use problem solving to investigate and understand increasingly complex mathematical content, including, but not limited to the ability to use problem-solving to develop ones own mathematical knowledge, reflect upon solutions and the problem-solving process, as well as refine strategies as needed. 2.Use mathematical proof, including, but not limited to, the ability to develop and evaluate mathematical conjectures, to construct and evaluate proofs and logical arguments to verify conjectures, to select and use various types of reasoning and methods of proof, and to demonstrate the capacity to articulate an understanding of how reasoning and proof are integral components of mathematics.

**MATH 601**

**Number Systems**

**(4 Credits)**

This course examines the structure and properties of mathematics while focusing on the development of mental mathematics strategies and problem solving skills. Topics include sets, functions, applications of rational numbers, integers, fractions, decimals, percentages, and number theory. Appropriate grade level techniques are utilized to investigate algorithms, probability and statistics, counting techniques, scientific notation, complex numbers, exponents, geometry, and measurement. Students will also investigate ratios, proportion, data analysis, patterns, and the connections to algebra and geometry topics in the context of the 5-12 grades mathematics curriculum.

**Prerequisite(s):**MATH 510 PreCalculus.

### View Course Outcomes:

- Demonstrate a capacity to use models to explore certain relationships, including magnitude, among fractions, decimals, percents, rations, and proportions
- Demonstrate knowledge of the historical development of number and number systems
- Apply, explain, and justify concepts in number and number theory
- Demonstrate computational proficiency and fluency, including the use of a variety of algorithms, estimation strategies, and mental mathematics techniques to judge the reasonableness of answers or approximate solutions
- Demonstrate knowledge of concepts and applications of limits and infinity
- Demonstrate a capacity to apply the concepts of proportional reasoning
- Demonstrate a capacity to make sense of large and small numbers and use scientific notation in mathematical and scientific modeling.

**MATH 602**

**Geometric Structures**

**(4 Credits)**

This course will examine concepts in Euclidean and non-Euclidean geometries. Course topics include area and volume, two- and three-dimensional perspective, congruence and similarity, properties of and relationships among geometric shapes and structures. Students will investigate graphing, vectors, motion, and symmetry. Students engage in course concepts through proofs, problem solving, dynamic geometric software, and through activities used in secondary and middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

**Prerequisite(s):**MATH 510 Pre-Calculus.

### View Course Outcomes:

- Build and manipulate representations of 2 and 3 dimensional objects and perceive an object from different perspectives.
- Analyze properties of and relationships among geometric shapes and structures.
- Apply transformations with connections to congruency and similarity.
- Demonstrate knowledge of non-Euclidean geometries and the historical development of the various geometries.
- Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry.
- Recognize measurement attributes and their effect on the choice of appropriate tools and units.
- Apply strategies, techniques, tools and formulas to determine measurements and their application in a variety of contexts.
- Demonstrate knowledge of the historical development of measurement and measurement systems.
- Employ estimation as a way of understanding measurement processes and units. 1
- Complete error analysis through determination of the reliability of numbers obtained from measurement. 1
- Understand and apply measurement conversion strategies. 1
- Apply geometric ideas and tools relating to the Pythagorean theorem, similar triangles, and trigonometry to solve problems. 1
- Use constructions, models, and dynamic geometric software to explore geometric relationships. 1
- Derive and explain formulas found in Euclidean geometry. 1
- Construct proofs using the axioms of Euclidean and non-Euclidean geometries.

**MATH 603**

**Probability and Statistics**

**(4 Credits)**

In this course students study topics in data analysis including: descriptive and inferential statistics, probability, odds and fair games, probability distributions, normal distributions, and estimation. Among the topics are numerical and graphical summaries for one and two variables, linear regression and correlation, confidence intervals and tests concerning means, sampling and experimentation, basic probability, confidence intervals, hypothesis testing, sampling distributions, two-sample t-tests for means, chi-squared tests, regress and correlation, and possible other topics. A standards statistical software package is used throughout the course to support the course format that includes: hands-on activities, computer-based simulations, creating and implementing student developed investigations, and actual secondary and middle school mathematics classroom activities. Throughout the course students are given opportunities to relate the mathematical concepts studied in this course to the mathematical concepts they will be teaching.

**Prerequisite(s):**MATH 502 Math for Our World.

### View Course Outcomes:

- Design investigations, collect data, display data in a variety of ways, and interpret data representations including bivariate data, conditional probability, and geometric probability.
- Use appropriate methods to estimate population characteristics, test conjectured relationships among variables, and analyze data.
- Use appropriate statistical methods and technology to analyze data and describe shape, spread, and center.
- Use both descriptive statistics to analyze data, make predictions, test hypotheses, and make decisions.
- Draw conclusions involving uncertainty by using hands-on and computer-based simulations.
- Apply probability concepts in identifying odds, fair games, mathematical expectation, and invalid conclusions.
- Judge the validity of a statistical argument, including evaluating the sample from which the statistics were developed and identify misuses of statistics.
- Demonstrate knowledge of the historical development of probability and statistics.
- Determine and compare experimental, theoretical, and conditional probabilities. 1
- Use statistical models to explore the connections between statistics and probability including correlation, regression, and analysis of variance. (Standard ~ 612.18 NH (7.a-j) ; Standard ~ 612017 NH (7.a-j))

**MATH 604**

**Linear Algebra**

**(4 Credits)**

This course examines concepts in algebra including: patterns and functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greater common divisor, inequalities, modular arithmetic and systems of numbers, properties of groups and fields, the field of complex numbers, polynomial arithmetic and algebra, linear equations. The course develops the mathematical structures, algebraic properties, and applications of matrices, determinants, vectors, vector spaces, systems of linear equations, and linear transformations. Students engage with these concepts through exploration, analysis, proof, and problem solving based on activities used in secondary and middle school mathematics. Throughout the course students are given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

**Prerequisite(s):**MATH 607 Calculus II.

### View Course Outcomes:

- Demonstrate a capacity to use physical materials and models to explore and explain the operations and properties of real and complex numbers with extensions to matrices and vectors.
- Identify and illustrate the mathematics underlying the theory of groups, rings, fields, and the relationships among them.
- Demonstrate a capacity to apply concepts of integer and rational exponents through modeling and applications. (Standard ~ 612.18 NH (4.h-j))
- Explain the distinctions among real numbers and their subsets with connection to field axioms.
- Demonstrate a capacity to apply the concepts of exponents, including integer and rational, through modeling and applications. (Standard ~ 612.17 NH (4.h-l))
- Model and analyze change and rates of change in various contexts.
- Use mathematical models to understand, represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships.
- Explore, analyze, and generalize a wide variety of patterns and functions using multiple representations including tables, graphs, written word, and symbolic rules.
- Represent information to solve problems using matrices.
- Using graphing utilities and other technological tools to represent, explain, and explore algebraic ideas including functions, equations, and expressions
- Demonstrate knowledge of the historical development of algebra
- Generalize patterns and functions using recursive and explicit representations
- Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities
- Understand and compare the properties of classes of functions and their inverses, including exponential, polynomial, rational, step, absolute value, root, logarithmic, and periodic, including trigonometric 1
- Understand and apply major concepts ofâ€ a. Linear algebra, including vector spaces and matrices; and b. Abstract algebra, including groups, rings, and fields 1
- Connect major concepts of linear and abstract algebra to the complex number system and other mathematical structures 1
- Understand, identify, and apply arithmetic and geometric sequences, including partial sums of infinite arithmetic and geometric sequences, with connections to linear and exponential functions. (Standard ~ 612.18 NH (6.a-l) ; Standard ~ 612.17 NH (6.a-l)

**MATH 605**

**Discrete Mathematics**

**(4 Credits)**

This course is designed to introduce students to discrete and abstract mathematical topics. Topics include propositional and predicate logic; elementary set theory; introduction to proof techniques including mathematical induction; sets, relations, functions, and relations; recurrence relations, graph theory, as well as the properties of groups, rings, and fields. Students study number systems, mathematical induction, algorithms and complex number systems, matrix manipulation, combinatorics, graph theory, and finite differences. Course activities are based on secondary and middle school mathematics curricula. This course considers the basic objects of mathematics through real-world examples and the methods used to elucidate their properties.

**Prerequisite(s):**MATH 606 Calculus I.

### View Course Outcomes:

- In the subject area of discrete mathematics, the candidate shall have the ability to: a. Apply the fundamental ideas of discrete mathematics in the formulation and solution of problems arising from real-world situations b. Use technology to solve problems involving the use of discrete structures
- In the subject area of discrete mathematics, the candidate shall demonstrate knowledge of: a. Historical development of discrete mathematics b. Basic elements of discrete mathematics, including but not limited to: i. Graph theory ii. Propositional logic iii. Mathematical induction iv. Recurrence relations v. Finite differences vi. Linear programming vii. Combinatorics (Standard ~ 612.18 NH (9.a-b) ; Standard ~ 612.17 NH (9.a-b)

**MATH 606**

**Calculus I**

**(4 Credits)**

This course is the first semester of a calculus sequence dealing with applications and modeling of the differential and integral calculus. The course focuses on functions and their graphs, limits, continuity, differentiation, integration, the derivative and its uses in optimization and mathematical modeling, as well as the Fundamental Theorem. Throughout the course students are given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts.

**Prerequisite(s):**MATH 510 Pre-Calculus or equivalent.

### View Course Outcomes:

- Use mathematical modeling and the concepts of calculus to represent and solve problems from real-world contexts.
- Use technology to explore and represent fundamental concepts of calculus.
- Demonstrate knowledge of the historical development of calculus.
- Understand and describe the connection of calculus to middle and high school mathematics topics.
- Demonstrate a conceptual understanding of and procedural facility with basic calculus concepts including limits, continuity, differentiation, and integration. (Standard ~ 612.18 NH (8.a-e) ; Standard ~ 612.17 NH (8.a-e)

**MATH 607**

**Calculus II**

**(4 Credits)**

This course is the second semester of a calculus sequence dealing with applications of differential and multivariable calculus. Topics include the calculus of transcendental functions, applications of integration, some differential equations, sequences and series, differentiation and integration of trigonometric functions multidimensional calculus with applications, and an introduction to multivariable calculus. Throughout the course students are given opportunities to relate the mathematical concepts studies to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts.

**Prerequisite(s):**MATH 606 Calculus I.

### View Course Outcomes:

- Demonstrate an understanding of basic concepts of multivariable calculus. (Standard ~ 612.18 NH (8.f)

**MATH 608**

**History of Mathematics**

**(4 Credits)**

This course addresses the historical development of major themes in mathematics, including calculation, numbers, geometry, algebra, infinity, and formalism in various civilizations ranging from the antiquity of Babylonia and Egypt through classical Greece, the Middle and Far East, and on to modern Europe. The course emphasizes how earlier civilizations influenced or failed to influence later ones and how the concepts evolved in these various civilizations. PREREQUISTE(S): MATH 606 Calculus I.

### View Course Outcomes:

- Develop and strengthen their conceptual knowledge of arithmetic, algebra, geometry, trigonometry and calculus through the study of why and how these concepts developed.
- Analyze how the development of mathematical concepts in different cultures influenced the development of those cultures and our present culture.
- Explore the influence of the development of mathematical concepts on other disciplines.
- Follow the development of mathematics from early number systems to the invention of calculus.
- Research historical questions and applications and present conclusions to others.

**MATH 609**

**Algebra Theory for Middle School Teachers**

**(4 Credits)**

This course will examine concepts in algebra including patterns and functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greatest common divisor, inequalities, modular arithmetic and systems of numbers, basic properties of groups and fields, and polynomial arithmetic and algebra. This course will develop mathematical structures, algebraic properties, and applications of matrices. Students will engage with these concepts through exploration, analysis, proof, and problem solving based on activities used in middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.

### View Course Outcomes:

- -Demonstrate a capacity to use physical materials and models to explore and explain the operations and properties of real and complex numbers with extensions to matrices and vectors. -Represent, use, and apply introductory concepts and properties of complex numbers. -Identify and illustrate the mathematics that underlies the procedures used for operations involving real numbers and their subsets. -Explain the distinctions among real numbers and their subsets with connection to field axioms. -Demonstrate a capacity to apply the concepts of exponents, including integer and rational, through modeling and applications. -Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry. -Model and analyze change and rates of change in various contexts. -Use mathematical models to understand, represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships. -Explore, analyze, and generalize a wide variety of patterns and functions using multiple representations including tables, graphs, written word, and symbolic rules. -Represent information and solve problems using matrices. -Use graphing utilities and other technological tools to represent, explain, and explore algebraic ideas including functions, equations, and expressions -Demonstrate knowledge of the historical development of algebra -Generalize patterns and functions using recursive and explicit representations -Understand, identify, and apply arithmetic and geometric sequences -Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities -Understand and compare the properties of classes of functions and their inverses, including exponential, polynomial, rational, step, absolute value, root, logarithmic, and periodic, including trigonometric -Represent and analyze group and field properties of real numbers and other mathematical structures

**MATH 700**

**Mathematical Proof for Educators**

**(4 Credits)**

This course introduces students to the language and methods used to create and write mathematical proofs and solve problems. Methods of proof will include: direct, contrapositive, contradiction, and induction. Methods of problem solving will be based on Polya’s four steps for solving problems. Students will learn about and utilize the many functions of proof including: verification, explanation, communication, discovery, justification, and inquiry. The course will also explore the relationship between problem solving and the process of proving. Students will explore fundamental abstract concepts in mathematics chosen from the following areas: functions and relations, set theory, number theory, and logic, Euclidian and non-Euclidian geometry, algebra, mathematical reasoning, proof, and problem solving. Connections to middle and secondary school mathematics curriculum emphasized. Students enrolled in this course at the 700 level will meet additional academic requirements including an applied project. PREREQUISITE: Pre-calculus

### View Course Outcomes:

- Use problem solving to investigate and understand increasingly complex mathematical content, including, but not limited to the ability to use problem solving to develop one’s own mathematical knowledge, reflect upon solutions and the problem solving process, as well as refine strategies as needed. Standard~612.18 NH (2.a.2,3,4); Standard ~ 612.17 NH (2.a.2)
- Use mathematical proof, including, but not limited to, the ability to develop and evaluate mathematical conjectures, to select and use various types of reasoning and methods of proof, and to demonstrate the capacity to articulate an understanding of how reasoning and proof are integral components of mathematics. (Standard ~ 612.18 NH (2.b.1,2,3,4) ; Standard ~ 612.17 NH (2.b.1,2,3,4)

**MATH 701**

**Number Systems**

**(4 Credits)**

This course examines the structure and properties of mathematics while focusing on the development of mental mathematics strategies and problem solving skills. Topics include sets, functions, applications of rational numbers, integers, fractions, decimals, percentages, and number theory. Appropriate grade level techniques are utilized to investigate algorithms, probability and statistics, counting techniques, scientific notation, complex numbers, exponents, geometry, and measurement. Students will also investigate ratios, proportion, data analysis, patterns, and the connections to algebra and geometry topics in the context of the 5-12 grades mathematics curriculum. PREREQUISITE: successful completion of PreCalculus.

### View Course Outcomes:

- Demonstrate a capacity to use models to explore certain relationships, including magnitude, among fractions, decimals, percents, rations, and proportions
- Demonstrate knowledge of the historical development of number and number systems
- Apply, explain, and justify concepts in number and number theory
- Demonstrate computational proficiency and fluency, including the use of a variety of algorithms, estimation strategies, and mental mathematics techniques to judge the reasonableness of answers or approximate solutions
- Demonstrate knowledge of concepts and applications of limits and infinity
- Demonstrate a capacity to apply the concepts of proportional reasoning
- Demonstrate a capacity to make sense of large and small numbers and use scientific notation in mathematical and scientific modeling (Standard ~ 612.18 NH (4.a-g) ; Standard ~ 612.17 NH (4.a-g)

**MATH 702**

**Geometric Structures for Teachers**

**(4 Credits)**

This course will examine concepts in Euclidean and non-Euclidean geometries. Course topics include area and volume, two- and three-dimensional perspective, congruence and similarity, properties of and relationships among geometric shapes and structures. Students will investigate graphing, vectors, motion and symmetry. Students engage in course concepts through proofs, problem solving, dynamic geometric software, and through activities used in secondary and middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. PREREQUISITE: successful completion of PreCalculus.

### View Course Outcomes:

- [Pivotal Standard] Solve problems involving Euclidean and non-Euclidean geometry and systems of measurement.
- [Pivotal Standard] Use constructions, models, and dynamic geometric software to explore geometric relationships.
- [Pivotal Standard] Derive and explain formulas found in Euclidean geometry.
- Construct proofs using the axioms of Euclidean and non-Euclidean geometries.
- Analyze and make connections between geometry concepts and the 5 – 12 mathematics curriculum.

**MATH 703**

**Probability and Statistics**

**(4 Credits)**

In this course students study topics in data analysis including descriptive and inferential statistics, probability, odds and fair games, probability distributions, normal distributions, and estimation. Among the topics are numerical and graphical summaries for one and two variables, linear regression and correlation, confidence intervals and tests concerning means, sampling and experimentation, basic probability, confidence intervals, hypothesis testing, sampling distributions, two-sample t-tests for means, chi-squared tests, regress and correlation, and possible other topics. A standards statistical software package is used throughout the course to support the course format that includes: hands-on activities; computer-based simulations; creating and implementing student developed investigations; and actual secondary and middle school mathematics classroom activities. Throughout the course students are given opportunities to relate the mathematical concepts studied in this course to the mathematical concepts they will be teaching. PREREQUISITE: successful completion of PreCalculus.

### View Course Outcomes:

- [Pivotal Standard] Design investigations, collect data, display data in a variety of ways, and interpret data representations including bivariate data, conditional probability and geometric probability.
- Use appropriate methods to estimate population characteristics, test conjectured relationships among variables, and analyze data.
- Use appropriate statistical methods and technology to analyze data and describe shape, spread, and center.
- [Pivotal Standard] Use both descriptive and inferential statistics to analyze data, make predictions, test hypotheses, and make decisions.
- Draw conclusions involving uncertainty by using hands-on and computer-based simulations.

**MATH 704**

**Linear Algebra**

**(4 Credits)**

This course will examine concepts in algebra including: Patterns and functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greatest common divisor, inequalities, modular arithmetic and systems of numbers, properties of groups and fields, the field of complex numbers, polynomial arithmetic and algebra, linear equations. Course will develop the mathematical structures, algebraic properties, and applications of matrices, determinants, vectors, vector spaces, systems of linear equations, and linear transformations. Students will engage with these concepts through exploration, analysis, proof, and problem solving based on activities used in secondary and middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. Students enrolled in this course at the 700 level will meet additional academic requirements including an applied project. PREREQUISITES: MATH 700 Mathematical Proof and MATH 707 Calculus II.

### View Course Outcomes:

- [Pivotal Standard] Demonstrate proficiency in linear and abstract algebra concepts, including vector spaces, matrices, groups, rings, and fields.
- [Pivotal Standard] Connect major concepts of linear and abstract algebra to the complex number systems and other mathematical structures.
- [Pivotal Standard] Identify and apply arithmetic and geometric sequences with connections to linear and exponential functions.
- Use mathematical models to understand, represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships.
- Using graphing utilities and other technological tools to represent, explain, and explore algebraic ideas including functions, equations, and expressions.
- Generalize patterns and functions using recursive and explicit representations.

**MATH 705**

**Discrete Mathematics**

**(4 Credits)**

This course is designed to introduce students to discrete and abstract mathematical topics. Topics include propositional and predicate logic; elementary set theory; introduction to proof techniques including mathematical induction; sets, relations, functions, and relations; recurrence relations, graph theory, as well as the properties of groups, rings, and fields. Students study number systems, mathematical induction, algorithms and complex number systems, matrix manipulation, combinatorics, graph theory, and finite differences. Course activities are based on secondary and middle school mathematics curricula. This course considers the basic objects of mathematics through real-world examples and the methods used to elucidate their properties. PREREQUISITE: MATH 706 Calculus I.

### View Course Outcomes:

- [Pivotal Standard] Apply the fundamental ideas of discrete mathematics in a formulation and solution of problems arising from real-world situations.
- Use technology to solve problems involving the use of discrete structures.
- [Pivotal Standard] Demonstrate knowledge of:
- Historical development of discrete mathematics
- Basic elements of discrete mathematics, including but not limited to: • Graph theory • Propositional logic • Mathematical induction • Recurrence relations • Finite differences • Linear programming • Combinatorics

**MATH 706**

**Calculus I**

**(4 Credits)**

The first semester of a calculus sequence dealing with applications and modeling of the differential and integral calculus. Course will focus on functions and their graphs, limits, continuity, differentiation, integration, the derivative and its uses in optimization and mathematical modeling, as well as the Fundamental Theorem. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts. Students enrolled in this course at the 700 level will meet additional academic requirements including an applied project. PREREQUISITE: Pre-calculus

### View Course Outcomes:

- [Pivotal Standard] Demonstrate a conceptual understanding of and procedural facility with basic calculus concepts including limits, continuity, differentiation, and integration.
- [Pivotal Standard] Use mathematical modeling and the concepts of calculus to represent and solve problems from real-world contexts.
- [Pivotal Standard] Use technology to explore and represent fundamental concepts of calculus.
- Demonstrate knowledge of the historical development of calculus.
- Describe the connection of calculus to middle and high school mathematics topics.

**MATH 707**

**Calculus II**

**(4 Credits)**

This course is the second semester of a calculus sequence dealing with applications of differential and multivariable calculus. Topics include the calculus of transcendental functions, applications of integration, some differential equations, sequences and series, differentiation and integration of trigonometric functions multidimensional calculus with applications, and an introduction to multivariable calculus. Throughout the course students are given opportunities to relate the mathematical concepts studies to the mathematical concepts they will be teaching. Graphing calculators are used throughout the course to explore and represent concepts. PREREQUISITE: MATH 706 Calculus I.

### View Course Outcomes:

- [Pivotal Standard] Demonstrate procedural facility with basic calculus concepts including integration techniques, sequences and series, parametric and polar curves, and vectors, and vector-valued functions.
- [Pivotal Standard] Use mathematical modeling and the concepts of calculus to represent and solve problems from real-world contexts.
- [Pivotal Standard] Use technology to explore and represent fundamental concepts of calculus.
- Demonstrate knowledge of the historical development of calculus.
- Describe the connection of calculus to middle and high school mathematics topics.
- Demonstrate an understanding of basic concepts of multivariable calculus.

**MATH 708**

**History of Mathematics**

**(4 Credits)**

This course addresses the historical development of major themes in mathematics, including calculation, numbers, geometry, algebra, infinity, and formalism in various civilizations ranging from the antiquity of Babylonia and Egypt through classical Greece, the Middle and Far East, and on to modern Europe. The course emphasizes how earlier civilizations influenced or failed to influence later ones and how the concepts evolved in these various civilizations. PREREQUISTE: MATH 706 Calculus I.

### View Course Outcomes:

- Develop and strengthen their conceptual knowledge of arithmetic, algebra, geometry, trigonometry and calculus through the study of why and how these concepts developed.
- Analyze how the development of mathematical concepts in different cultures influenced the development of those cultures and our present culture.
- Learners will explore the influence of the development of mathematical concepts on other disciplines.
- Follow the development of mathematics from early number systems to the invention of calculus
- Research historical questions and applications and present conclusions to others.

**MATH 709**

**Algebra Theory for Teachers**

**(4 Credits)**

This course will examine concepts in Algebra including patterns, functions, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greatest common division, inequalities, basic properties of groups and fields, and polynomial arithmetic and algebra. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching. PREREQUISITES: MATH 700 Mathematical Proof and MATH 706 Calculus I.

### View Course Outcomes:

- In the subject area of number and operations, the candidate shall have the ability to: -Demonstrate a capacity to use physical materials and models to explore and explain the operations and properties of real and complex numbers with extensions to matrices and vectors. -Represent, use, and apply introductory concepts and properties of complex numbers; -Identify and illustrate the mathematics that underlies the procedures used for operations involving real numbers and their subsets; -Explain the distinctions among real numbers and their subsets with connection to field axioms -Demonstrate a capacity to apply the concepts of exponents, including integer and rational, through modeling and applications
- In the subject area of geometry and measurement, the candidate shall have the ability to: -Connect the ideas of algebra and geometry through the use of coordinate geometry, graphing, vectors, and motion geometry
- In the subject area of functions and algebra, the candidate shall have the ability to: -Model and analyze change and rates of change in various contexts -Use mathematical models to understand, represent, and communicate quantitative relationships, including, but not limited to equality, equations, inequalities, and proportional relationships -Explore, analyze, and generalize a wide variety of patterns and functions using multiple representations including tables, graphs, written word, and symbolic rules; -Represent information and solve problems using matrices -Use graphing utilities and other technological tools to represent, explain, and explore algebraic ideas including functions, equations, and expressions -Demonstrate knowledge of the historical development of algebra -Generalize patterns and functions using recursive and explicit representations -Understand, identify, and apply arithmetic and geometric sequences -Articulate the meaning of functions and their inverse relationships, both formally and informally, with the use of concrete materials and graphing utilities -Understand and compare the properties of classes of functions and their inverses, including exponential, polynomial, rational, step, absolute value, root, logarithmic, and periodic, including trigonometric Represent and analyze group and field properties of real numbers and other mathematical structures